A note on sensitivity of semigroup actions
By E. Kontorovich, Michael Megrelishvili. 2006
96 citations recorded by the source corpus.
Abstract It is well known that for a transitive dynamical system (X,f) sensitivity to initial conditions follows from the assumption that the periodic points are dense. This was done by several authors: Banks, Brooks, Cairns, Davis and Stacey (Am. Math. Mon. 99, 332–334, 1992), Silverman (Rocky Mt. J. Math. 22, 353–375, 1992) and Glasner and Weiss (Nonlinearity 6, 1067–1075, 1993). In the latter article Glasner and Weiss established a stronger result (for compact metric systems) which implies that a transitive non-minimal compact metric system (X,f) with dense set of almost periodic points is sensitive. This is true also for group actions as was proved in the book of Glasner (Ergodic Theory via Joinings, 2003). Our aim is to generalize these results in the frame of a unified approach for a wide class of topological semigroup actions including one-parameter semigroup actions on Polish spaces.
Subfields: Control and Systems Engineering, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b93c80a26bec24a16c5c7f372d3a86aea7b58a38
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In Control and Systems Engineering
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Sensitivity and devaney’s chaos in uniform spaces (2011, background): “In the case when X is a metric space, the preceding result was first obtained in [1] and [7] for G = Z, and in [6] for an arbitrary group G.”